Inverse Modeling and Animation of Growing Single-stemmed Trees at Interactive Rates

Abstract

For city planning purposes, animations of growing trees of several species can be used to deduce which species may best fit a particular environment. The models used for the animation must conform to real measured data. We present an approach for inverse modeling to fit global growth parameters. The model comprises local production rules, which are iteratively and simultaneously applied to build a fractal branching structure, and incorporates the propensity of trees to grow towards light. The parameters of the local production rules are derived from global functions that describe the measured tree growth data over time. The production rules are influenced by the global light distribution, which is represented by the amount of light available at each position within the tree’s crown. Since we want to allow the user to explore the tree’s appearance interactively at any time during the animation, all modeling computations must be within a time frame that allows for interactive rendering rates. To this end, we developed a fast approximate algorithm for computing the light distribution. The rendering itself must also be fast; therefore, we sought a well-balanced compromise between photo-realism and performance. Because shadow computations play a key role for photo-realism, we developed a fast approximate shadow computation algorithm including soft shadows and self-shadowing. We applied our methods in order to model and animate the growth of seven single-stemmed tree species in an interactive setting.